how many different three letter passwords can be formed from the letters A,B,C,D,E,F, and G if no repetition of letters is allowed

Question

how many different three letter passwords can be formed from the letters A,B,C,D,E,F, and G if no repetition of letters is allowed

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Sarah 27 mins 2021-10-14T00:49:29+00:00 1 Answer 0

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    2021-10-14T00:50:36+00:00

    Answer:

    There are 210 possible three-letter passwords

    Step-by-step explanation:

    We have 7 different letters. One example of a valid 3-letter password would be CFB. This other password EDE is not allowed because the E is repeated.

    We need to find all the possible forms to have 3 different ordered letters out of 7 options.

    We can place any valid letter as the first one like BXX. It can be done in 7 ways since we have them all available. Now we can replace the first X with the second letter, but now B is used, so we only 6 have six letters to use. That gives us 7×6= 42 combinations. Finally, the second X can be chosen from the remaining 5 letters. The answer is then

    There are 7x6x5=210 possible three-letter different passwords

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